The request was made during a meeting between European justice Commissioner Vĕra Jourová and Volkswagen CEO Matthias Müller, with Müller reportedly agreeing to discuss compensation again at a meeting later this month.
The decision has promoted some Socialist MEPs to push for stronger rights for car consumers.
The Volkswagen refusal to pay out compensation to EU customers over the dieselgate vehicle emissions scandal comes despite the German company having agreed a $10bn settlement with drivers in the US.
Since the scandal broke, Volkswagen has admitted to installing cheating software on nearly 11 million diesel vehicles world-wide.
The company pleaded guilty to fraud in the US and agreed to pay nearly $25bn in fines, penalties and compensation.
Earlier this week, Jourová met with consumer protection authorities to decide on joint enforcement action against VW, whereby the company could face legal action in national courts for alleged breaches of EU law, including the unfair commercial practices directive and sales and guarantees directive.
Next month, British S&D group MEP Seb Dance will table an amendment on behalf of his group calling for greater consumer rights for affected car buyers. The report recommends EU countries "do more to monitor manufacturers" and enforce existing measures already in place.
Dance is Labour's spokesperson on the environment committee and the S&D group spokesperson on the committee of inquiry into emission measurement in the automotive sector, which was created to probe the emissions testing scandal. The committee is due to conclude its work later this year.
Dance said, "It is plainly unfair that Volkswagen has compensated US customers over the dieselgate scandal, but not Europeans. Jourová is absolutely right to coordinate national agencies to take action over the litany of failures that led to dieselgate, and to seek redress for EU consumers.
"The S&D group has led calls for strong EU action over the dieselgate scandal, and we urge all MEPs to back our proposals for greater consumer rights when the European Parliament votes on the emissions report in April."
He added, "The UK government must back this action, and maintain EU consumer rights after Brexit, and match any strengthening of those rights."
Meanwhile, German chancellor Angela Merkel is to give evidence to a committee set up by the German parliament to determine whether she and her government knew of problems with Volkswagen diesel engines years before US regulators in September 2015 disclosed it had rigged engines to cheat on tough US emissions tests. Of the affected vehicles, about 2.6 million of them were sold in Germany.
Her decision to give evidence to the committee comes after in the wake of claims that excess air pollution caused by the Volkswagen emissions cheating is on track to cause health problems that could shorten 1200 lives in Europe.
Researchers mapped out the increased population exposure to fine particles during the time Volkswagen was selling the affected vehicles against the likely health effects of the exposure. They found that 1200 lives would be shortened because of the increased air pollution caused by the cheating, resulting in 13,000 years of life lost and costing €1.9bn in lost life-years.
The European Environmental Agency (EEA) estimates that outdoor air pollution shortens 400,000 lives a year in Europe, and the researchers say that pollution exacerbates asthma.